Question

Three conducting spherical shells have charges $q,-2q$ and $3q$ as shown in figure. Electric potential at point $\text{P}$ is

• A. $kq(\frac{1}{R}+\frac{1}{r})$
• B. $kq(\frac{1}{R}-\frac{1}{r})$
• C. $\frac{kq}{3R}$
• D. $\frac{kq}{r}$

Answer 1

The correct option is B $kq(\frac{1}{R}-\frac{1}{r})$

Potential at $\text{P}$,

$V_P=V_q+V_{-2q}+V_{3q}$

using formula of potential of uniformly charged shell

$\Rightarrow V_P=\frac{kq}{r}-\frac{k\left(2q\right)}{r}+\frac{k\left(3q\right)}{3R}$

$\Rightarrow V_P=kq(\frac{1}{R}-\frac{1}{r})$

So, option $\left(b\right)$ is correct.

Why this question ? Concept - Electric potential on the surface and at any point inside the shell is equal and given by $V=\frac{kq}{R}$, ($R=$ radius of shell)